Added(A)/Deleted(D) following books

 A  Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/README.txt
A  Numerical_Methods_by_E._Balaguruswamy/chapter10.ipynb
A  Numerical_Methods_by_E._Balaguruswamy/chapter11.ipynb
A  Numerical_Methods_by_E._Balaguruswamy/chapter12.ipynb
A  Numerical_Methods_by_E._Balaguruswamy/chapter13.ipynb
A  Numerical_Methods_by_E._Balaguruswamy/chapter14.ipynb
A  Numerical_Methods_by_E._Balaguruswamy/chapter15.ipynb
A  Numerical_Methods_by_E._Balaguruswamy/chapter3.ipynb
A  Numerical_Methods_by_E._Balaguruswamy/chapter4.ipynb
A  Numerical_Methods_by_E._Balaguruswamy/chapter6.ipynb
A  Numerical_Methods_by_E._Balaguruswamy/chapter7.ipynb
A  Numerical_Methods_by_E._Balaguruswamy/chapter8.ipynb
A  Numerical_Methods_by_E._Balaguruswamy/chapter9.ipynb
A  Numerical_Methods_by_E._Balaguruswamy/screenshots/greatest-precision-4.png
A  Numerical_Methods_by_E._Balaguruswamy/screenshots/rounding-off-4.png
A  Numerical_Methods_by_E._Balaguruswamy/screenshots/truncation-error-4.png
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_4JhcI7F.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_5CfOfQx.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_B30VPml.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_BE8QjoS.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_Gb015bo.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_KQ8ycMr.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_LIZWeY4.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_Opo6g3L.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_Pq40WOu.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_QLXi0uM.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_TdOIeIQ.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_UiM06tF.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_VQabJzR.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_XKPPUxj.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_dfFlLnm.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_fegIkl6.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_g1GxlUN.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_gGvuusH.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_gZeNd4b.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_khAt4Y6.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_oJQM5Mb.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_p22tFeA.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_qNHcrb8.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_qeUxd0G.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_r0nfWNs.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_uWQUwaW.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_vkMAnbH.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_wP2wGMS.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_x09tDSO.ipynb
A  Physics_BSc(Paper_4)_by_Sanjeeva_Rao,_Bhikshmaiah,_Ramakrishna_Reddy,_Ananta_Ramaiah/C_yCW2orc.ipynb

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diff --git a/Numerical_Methods_by_E._Balaguruswamy/chapter11.ipynb b/Numerical_Methods_by_E._Balaguruswamy/chapter11.ipynb
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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Chapter 11 - Numerical differentiation"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Example No. 11_01 Pg No. 348"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "h\ty\terr\n",
+      "0.2 \t2.2 \t0.2\n",
+      "0.1 \t2.1 \t0.1\n",
+      "0.05 \t2.05 \t0.05\n",
+      "0.01 \t2.01 \t0.01\n"
+     ]
+    }
+   ],
+   "source": [
+    "from __future__ import division\n",
+    "from scipy.misc import derivative\n",
+    "\n",
+    "#First order forward difference\n",
+    "\n",
+    "def f(x):\n",
+    "    F=x**2\n",
+    "    return F\n",
+    "                 \n",
+    "\n",
+    "def df(x,h):\n",
+    "    DF=(f(x+h)-f(x))/h\n",
+    "    return DF\n",
+    "\n",
+    "dfactual = derivative(f,1)\n",
+    "h = [0.2, 0.1, 0.05, 0.01 ]\n",
+    "print 'h\\ty\\terr'\n",
+    "for hh in h:\n",
+    "    y = df(1,hh)\n",
+    "    err = y - dfactual\n",
+    "    print hh,'\\t',y,'\\t',err"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Example No. 11_02 Pg No. 350"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "h\ty\terr\n",
+      "0.2 \t2.0 \t-4.4408920985e-16\n",
+      "0.1 \t2.0 \t4.4408920985e-16\n",
+      "0.05 \t2.0 \t4.4408920985e-16\n",
+      "0.01 \t2.0 \t1.7763568394e-15\n"
+     ]
+    }
+   ],
+   "source": [
+    "from __future__ import division\n",
+    "from scipy.misc import derivative\n",
+    "\n",
+    "#Three-Point Formula\n",
+    "\n",
+    "def f(x):\n",
+    "    F = x**2\n",
+    "    return F\n",
+    "def df(x,h):\n",
+    "    DF = (f(x+h)-f(x-h))/(2*h)\n",
+    "    return DF\n",
+    "dfactual = derivative(f,1)\n",
+    "h = [0.2, 0.1, 0.05, 0.01 ]\n",
+    "print 'h\\ty\\terr'\n",
+    "for hh in h:\n",
+    "    y = df(1,hh)\n",
+    "    err = y - dfactual\n",
+    "    print hh,'\\t',y,'\\t',err\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Example No. 11_03 Pg No. 353"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "h\ty\t\terr\n",
+      "0.01 \t0.898257285429 \t-0.00218981692372\n",
+      "0.015 \t0.897151155627 \t-0.00329594672573\n",
+      "0.02 \t0.896037563392 \t-0.00440953896077\n",
+      "0.025 \t0.894916522709 \t-0.00553057964367\n",
+      "0.03 \t0.893788047675 \t-0.00665905467759\n",
+      "0.035 \t0.892652152498 \t-0.00779494985432\n",
+      "0.04 \t0.891508851498 \t-0.00893825085448\n",
+      "\n",
+      "M2 = 2.061e-08 & hopt = 4.706e-01\n"
+     ]
+    }
+   ],
+   "source": [
+    "from __future__ import division\n",
+    "from scipy.misc import derivative\n",
+    "from numpy import arange,sin,cos,sqrt\n",
+    "x = 0.45#\n",
+    "def f(x):\n",
+    "    F = sin(x)\n",
+    "    return F\n",
+    "def df(x,h):\n",
+    "    DF = (f(x+h) - f(x))/h\n",
+    "    return DF\n",
+    "dfactual =  cos(x)#\n",
+    "h = arange(0.01,0.005+0.04,0.005)\n",
+    "n = len(h)#\n",
+    "print 'h\\ty\\t\\terr'\n",
+    "for hh in h:\n",
+    "    y = df(x,hh)\n",
+    "    err = y - dfactual \n",
+    "    print hh,'\\t',y,'\\t',err\n",
+    "\n",
+    "#using 16 significant digits so the bound for roundoff error is 0.5*10**(-16)\n",
+    "e = 0.5*10**(-16)\n",
+    "M2 = max(sin(x+h))#\n",
+    "hopt = 2*sqrt(e/M2)#\n",
+    "print '\\nM2 = %.3e & hopt = %.3e'%(hopt,M2)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Example No. 11_04 Pg No. 354"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      " d2fexact = -0.732 \n",
+      " err = -6.097e-06 \n",
+      " y = -0.732 \n"
+     ]
+    }
+   ],
+   "source": [
+    "from __future__ import division\n",
+    "from numpy import arange,sin,cos,sqrt\n",
+    "\n",
+    "#Approximate second derivative\n",
+    "\n",
+    "x = 0.75#\n",
+    "h = 0.01#\n",
+    "def f(x):\n",
+    "    F = cos(x)\n",
+    "    return F\n",
+    "def d2f(x,h):\n",
+    "    D2F = ( f(x+h) - 2*f(x) + f(x-h) )/h**2\n",
+    "    return D2F\n",
+    "y = d2f(0.75,0.01)#\n",
+    "d2fexact = -cos(0.75)\n",
+    "err = d2fexact - y #\n",
+    "print ' d2fexact = %.3f \\n err = %.3e \\n y = %.3f '%(d2fexact,err,y)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Example No. 11_05 Pg No. 358"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "v(5) =  4.25\n",
+      "v(7) =  5.5\n",
+      "v(9) =  6.75\n"
+     ]
+    }
+   ],
+   "source": [
+    "#Differentiation of tabulated data\n",
+    "\n",
+    "T = range(5,10)\n",
+    "s = [10,  14.5,  19.5,  25.5 , 32 ]\n",
+    "h = T[1]-T[0]\n",
+    "n = len(T)\n",
+    "def v(t):\n",
+    "    if t in T and T.index(t) == 0:\n",
+    "        V = (-3*s[T.index(t) ] + 4*s[T.index(t+h)]  - s[T.index(t+2*h) ] ) /(2*h) #Three point forward difference formula\n",
+    "    elif t in T and T.index(t) == n-1:\n",
+    "        V = ( 3*s[T.index(t)] - 4*s[ T.index(t-h)]  + s[T.index(t-2*h) ]  )/(2*h) #Backward difference formula\n",
+    "    else:\n",
+    "        V = ( s[T.index(t+h)]  - s[T.index(t-h)]  )/(2*h) #Central difference formula\n",
+    "    return V\n",
+    "\n",
+    "v_5 = v(5)\n",
+    "v_7 = v(7)\n",
+    "v_9 = v(9)\n",
+    "\n",
+    "print 'v(5) = ',v_5\n",
+    "print 'v(7) = ',v_7\n",
+    "print 'v(9) = ',v_9\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Example No. 11_06 Pg No. 359"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "a(7) =  0.5\n"
+     ]
+    }
+   ],
+   "source": [
+    "T = range(5,10)\n",
+    "s = [10,  14.5 , 19.5 , 25.5,  32 ]\n",
+    "h = T[1]-T[0]\n",
+    "def a(t):\n",
+    "    A = ( s[T.index(t+h) ] - 2*s[ T.index(t) ] + s[T.index(t-h)  ] )/h**2\n",
+    "    return A\n",
+    "a_7 = a(6)\n",
+    "\n",
+    "print 'a(7) = ',a_7"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Example No. 11_7 Pg No. 359"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "solving the above equations we get \n",
+      "\n",
+      " y1 = y(0.25) = -0.117562 \n",
+      " y2 = y(0.5) = -0.168475 \n",
+      " y3 = y(0.75) = -0.139088 \n",
+      " \n"
+     ]
+    }
+   ],
+   "source": [
+    "from numpy import mat,divide,linalg\n",
+    "h = 0.25 #\n",
+    "#y''(x) = e**(x**2)\n",
+    "#y(0) = 0 , y(1) = 0\n",
+    "# y''(x) = y(x+h) - 2*y(x) + y(x-h)/h**2  = e**(x**2)\n",
+    "#( y(x + 0.25) - 2*y(x) + y(x-0.25) )/0.0625 = e**(x**2)\n",
+    "#y(x+0.25) - 2*y(x) + y(x - 0.25) = 0.0624*e**(x**2)\n",
+    "#y(0.5) - 2*y(0.25) + y(0) = 0.0665\n",
+    "#y(0.75) - 2*y(0.5) + y(0.25) = 0.0803\n",
+    "#y(1) - 2*y(0.75) + y(0.5) = 0.1097\n",
+    "#given y(0) = y(1) = 0\n",
+    "#\n",
+    "#0 + y2 - 2y1 = 0.06665\n",
+    "#y3 - 2*y2 + y1 = 0.0803\n",
+    "#-2*y3 + y2 + 0 = 0.1097\n",
+    "#Therefore\n",
+    "A = mat([[0, 1, -2],[1, -2, 1],[-2, 1, 0 ]])\n",
+    "B = mat([[ 0.06665],[0.0803] ,[0.1097 ]])\n",
+    "C = linalg.solve(A,B)\n",
+    "print 'solving the above equations we get \\n\\n y1 = y(0.25) = %f \\n y2 = y(0.5) = %f \\n y3 = y(0.75) = %f \\n '%(C[2],C[1],C[0])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Example No. 11_08 Pg No. 362"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "richardsons technique -\n",
+      "\n",
+      "df(0.5) =  1.64850499031\n",
+      "D(rh) = D(0.25) =  1.71828182846\n",
+      "D(0.5) =  1.66594919985\n",
+      "Exact df(0.5) =  1.93757920531\n",
+      "The result by richardsons technique is much better than other results\n",
+      "for r = 2\n",
+      "df(x) =  1.64518270284\n",
+      "D(rh) =  1.93757920531\n"
+     ]
+    }
+   ],
+   "source": [
+    "from numpy import arange,exp\n",
+    "from scipy.misc import derivative\n",
+    "\n",
+    "x = arange(-0.5,0.25+1.5,0.25)\n",
+    "h = 0.5 ;\n",
+    "r = 1.0/2 ;\n",
+    "\n",
+    "def f(x):\n",
+    "    F = exp(x)\n",
+    "    return F\n",
+    "def D(x,h):\n",
+    "    D = (f(x + h) - f(x-h) )/(2*h) \n",
+    "    return D\n",
+    "def df(x,h,r):\n",
+    "    Df = (D(x,r*h) - r**2*D(x,h))/(1-r**2)\n",
+    "    return Df\n",
+    "\n",
+    "df_05 = df(0.5,0.5,1.0/2);\n",
+    "print 'richardsons technique -\\n\\ndf(0.5) = ',df_05\n",
+    "print 'D(rh) = D(0.25) = ',D(0.5,0.5)\n",
+    "print 'D(0.5) = ',D(0.5,0.25)\n",
+    "\n",
+    "dfexact = derivative(f,0.5)\n",
+    "print 'Exact df(0.5) = ',dfexact\n",
+    "print 'The result by richardsons technique is much better than other results'\n",
+    "\n",
+    "#r = 2\n",
+    "print 'for r = 2'\n",
+    "print 'df(x) = ',df(0.5,0.5,2)\n",
+    "print 'D(rh) = ',D(0.5,2*0.5)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}